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# A C# Implementation of Douglas-Peucker Line Approximation Algorithm

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6 Jun 2007MIT 154.8K   3.5K   60   39
DP Line approximation algorithm is a well-known method to approximate 2D lines. It is quite fast, O(nlog_2(n)) for a n-points line and can drastically compress a data curve. Here, a fully OOP implementation is given.

## Introduction

I have found multiple implementations of the Douglas-Peucker algorithm but not in any .NET language, so I decided to port it over. Jonathan de Halleux has a wonderful explanation here.

## Background

I needed to reduce polygons size to display on a map based on zoom levels.

## Using the Code

The code included is complete and should run out of the box in Visual Studio 2005. If it does not, please let me know.

C#
```/// <summary>
/// Uses the Douglas Peucker algorithm to reduce the number of points.
/// </summary>
/// <param name="Points">The points.</param>
/// <param name="Tolerance">The tolerance.</param>
/// <returns></returns>
public static List<Point> DouglasPeuckerReduction
(List<Point> Points, Double Tolerance)
{
if (Points == null || Points.Count < 3)
return Points;

Int32 firstPoint = 0;
Int32 lastPoint = Points.Count - 1;
List<Int32> pointIndexsToKeep = new List<Int32>();

//Add the first and last index to the keepers

//The first and the last point cannot be the same
while (Points[firstPoint].Equals(Points[lastPoint]))
{
lastPoint--;
}

DouglasPeuckerReduction(Points, firstPoint, lastPoint,
Tolerance, ref pointIndexsToKeep);

List<Point> returnPoints = new List<Point>();
pointIndexsToKeep.Sort();
foreach (Int32 index in pointIndexsToKeep)
{
}

return returnPoints;
}

/// <summary>
/// Douglases the peucker reduction.
/// </summary>
/// <param name="points">The points.</param>
/// <param name="firstPoint">The first point.</param>
/// <param name="lastPoint">The last point.</param>
/// <param name="tolerance">The tolerance.</param>
/// <param name="pointIndexsToKeep">The point index to keep.</param>
private static void DouglasPeuckerReduction(List<Point>
points, Int32 firstPoint, Int32 lastPoint, Double tolerance,
ref List<Int32> pointIndexsToKeep)
{
Double maxDistance = 0;
Int32 indexFarthest = 0;

for (Int32 index = firstPoint; index < lastPoint; index++)
{
Double distance = PerpendicularDistance
(points[firstPoint], points[lastPoint], points[index]);
if (distance > maxDistance)
{
maxDistance = distance;
indexFarthest = index;
}
}

if (maxDistance > tolerance && indexFarthest != 0)
{
//Add the largest point that exceeds the tolerance

DouglasPeuckerReduction(points, firstPoint,
indexFarthest, tolerance, ref pointIndexsToKeep);
DouglasPeuckerReduction(points, indexFarthest,
lastPoint, tolerance, ref pointIndexsToKeep);
}
}

/// <summary>
/// The distance of a point from a line made from point1 and point2.
/// </summary>
/// <param name="pt1">The PT1.</param>
/// <param name="pt2">The PT2.</param>
/// <param name="p">The p.</param>
/// <returns></returns>
public static Double PerpendicularDistance
(Point Point1, Point Point2, Point Point)
{
//Area = |(1/2)(x1y2 + x2y3 + x3y1 - x2y1 - x3y2 - x1y3)|   *Area of triangle
//Base = v((x1-x2)²+(x1-x2)²)                               *Base of Triangle*
//Area = .5*Base*H                                          *Solve for height
//Height = Area/.5/Base

Double area = Math.Abs(.5 * (Point1.X * Point2.Y + Point2.X *
Point.Y + Point.X * Point1.Y - Point2.X * Point1.Y - Point.X *
Point2.Y - Point1.X * Point.Y));
Double bottom = Math.Sqrt(Math.Pow(Point1.X - Point2.X, 2) +
Math.Pow(Point1.Y - Point2.Y, 2));
Double height = area / bottom * 2;

return height;

//Another option
//Double A = Point.X - Point1.X;
//Double B = Point.Y - Point1.Y;
//Double C = Point2.X - Point1.X;
//Double D = Point2.Y - Point1.Y;

//Double dot = A * C + B * D;
//Double len_sq = C * C + D * D;
//Double param = dot / len_sq;

//Double xx, yy;

//if (param < 0)
//{
//    xx = Point1.X;
//    yy = Point1.Y;
//}
//else if (param > 1)
//{
//    xx = Point2.X;
//    yy = Point2.Y;
//}
//else
//{
//    xx = Point1.X + param * C;
//    yy = Point1.Y + param * D;
//}

//Double d = DistanceBetweenOn2DPlane(Point, new Point(xx, yy));
}```

## Points of Interest

The code is not overly complicated. It was fun to port this algorithm, since all I feel I do nowadays is hold business' hands to help them try and solve business problems that there is no consensus on.

## History

• Beta 1

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 First PrevNext
 More efficient version in Loyc.Math + Bug fix Qwertie22-Nov-23 10:03 Qwertie 22-Nov-23 10:03
 Addition to get rid of possible StackOverflow Exception Alexander Panfilenok12-Oct-23 5:08 Alexander Panfilenok 12-Oct-23 5:08
 Thanks! Keith Rule21-May-22 9:19 Keith Rule 21-May-22 9:19
 Re: rejecting recursion + distance calc acceleration TerrySpiderman21-Mar-17 3:05 TerrySpiderman 21-Mar-17 3:05
 to save stack memory with great amount of points and tolerance near zero i prefer to reject recursion adevder18-Feb-17 1:22 adevder 18-Feb-17 1:22
 Nice veen_rp18-Apr-16 19:41 veen_rp 18-Apr-16 19:41
 If (first = last) Bug! Giovani Luigi14-Dec-15 12:44 Giovani Luigi 14-Dec-15 12:44
 Re: If (first = last) Bug! Keith Rule21-May-22 13:40 Keith Rule 21-May-22 13:40
 Thanks for this comment. It saved me from having to troubleshoot that weird last point being off in some random direction issue. This fix solved the problem. Thanks for saving me a bunch of troubleshooting. Keith Rule
 DouglasPeuckerN() conversion? cbordeman11-Dec-15 17:42 cbordeman 11-Dec-15 17:42
 Re: DouglasPeuckerN() conversion? Mr Lorenz27-Apr-17 7:44 Mr Lorenz 27-Apr-17 7:44
 Useful Dineshkumar_MCA22-Apr-15 2:18 Dineshkumar_MCA 22-Apr-15 2:18
 BUG tolerance Member 1017584518-Feb-15 2:08 Member 10175845 18-Feb-15 2:08
 Thanks + pruned code Stoyan Haralampiev23-Oct-14 3:30 Stoyan Haralampiev 23-Oct-14 3:30
 Using this algorithm on data from database Saket Surya2-Jun-14 3:38 Saket Surya 2-Jun-14 3:38
 Point projected on the line but behind the segment? Bug? Sergiy Tkachuk25-Mar-14 14:31 Sergiy Tkachuk 25-Mar-14 14:31
 About Tolerance kamlesh Prajapati8-Jan-14 23:55 kamlesh Prajapati 8-Jan-14 23:55
 Why do you create your own Point? leiyangge3-Jan-14 22:37 leiyangge 3-Jan-14 22:37
 License Diego Catalano14-Dec-13 2:42 Diego Catalano 14-Dec-13 2:42
 1 bug, + 1 potential bug gyuri1023-Apr-12 23:45 gyuri10 23-Apr-12 23:45
 Re: 1 bug, + 1 potential bug tplokas26-Mar-13 14:46 tplokas 26-Mar-13 14:46
 Useful,Thanks! masy19112-Mar-12 23:43 masy191 12-Mar-12 23:43
 Great Job! Christopher Drake19-Dec-11 8:32 Christopher Drake 19-Dec-11 8:32
 how calculate an epsilon value unravel-the-sky23-May-11 6:52 unravel-the-sky 23-May-11 6:52
 Some Issues with your implementation MattMi15-Jul-10 11:57 MattMi 15-Jul-10 11:57
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